Photon



Photon

Photons emitted in a coherent beam from a laser
Composition: Gauge boson
Interaction: Electromagnetic
Theorized: Albert Einstein (1905–17)
Symbol: γ or hν
Mass: 0[1]
Mean lifetime: Stable[2]
Electric charge: 0
Spin: 1[1]

In physics, the photon is the wave–particle duality”). Photons show wave-like phenomena, such as refraction by a lens and destructive interference when reflected waves cancel each other out; however, as a particle, it can only interact with matter by transferring the amount of energy

E = \frac{hc}{\lambda},

where h is Planck's constant, c is the photoreceptor cell of an eye, thus contributing to vision.[4]

Apart from having energy, a photon also carries polarization. It follows the laws of quantum mechanics, which means that often these properties do not have a well-defined value for a given photon. Rather, they are defined as a probability to measure a certain polarization, position, or momentum. For example, although a photon can excite a single molecule, it is often impossible to predict beforehand which molecule will be excited.

The above description of a photon as a carrier of electromagnetic radiation is commonly used by physicists. However, in theoretical physics, a photon can be considered as a mediator for any type of electromagnetic interactions, including magnetic fields and electrostatic repulsion between like charges.

The modern concept of the photon was developed gradually (1905–17) by Albert Einstein[5][6][7][8] to explain experimental observations that did not fit the classical thermal equilibrium. Other physicists sought to explain these anomalous observations by semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light are quantized. Although these semiclassical models contributed to the development of quantum mechanics, further experiments proved Einstein's hypothesis that light itself is quantized; the quanta of light are photons.

The photon concept has led to momentous advances in experimental and theoretical physics, such as charge, mass and spin—are determined by the properties of this gauge symmetry.

The concept of photons is applied to many areas such as measurements of molecular distances. Recently, photons have been studied as elements of quantum computers and for sophisticated applications in optical communication such as quantum cryptography.

Nomenclature

The photon was originally called a “light quantum” (das Lichtquant) by Albert Einstein.[5] The modern name “photon” derives from the Greek word for light, φῶς, (transliterated phôs), and was coined in 1926 by the physical chemist Arthur Compton with defining quanta of light as photons in 1927.[10][11]

In physics, a photon is usually denoted by the symbol γ, the Greek letter gamma. This symbol for the photon probably derives from chemistry and optical engineering, photons are usually symbolized by hν, the energy of a photon, where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f.

Physical properties

 

See also: Special relativity

The photon is massless,[3] has no gauge boson for electromagnetism, and therefore all other quantum numbers—such as lepton number, baryon number, or strangeness—are exactly zero.

Photons are emitted in many natural processes, e.g., when a charge is accelerated, during a molecular, atomic or nuclear transition to a lower energy level, or when time-reversed processes which correspond to those mentioned above: for example, in the production of particle–antiparticle pairs or in molecular, atomic or nuclear transitions to a higher energy level.

In empty space, the photon moves at c (the momentum p are related by E = cp, where p is the magnitude of the momentum. For comparison, the corresponding equation for particles with a mass m is E2 = c2p2 + m2c4, as shown in special relativity.

The energy and momentum of a photon depend only on its frequency ν or, equivalently, its wavelength λ

E = \hbar\omega = h\nu = \frac{h c}{\lambda}
\mathbf{p} = \hbar\mathbf{k}

and consequently the magnitude of the momentum is

p = \hbar k = \frac{h}{\lambda} = \frac{h\nu}{c}

where \hbar = h/2\pi \! (known as Dirac's constant or Planck's reduced constant); k is the wave vector (with the wave number k = 2π / λ as its magnitude) and ω = 2πν is the angular frequency. Notice that k points in the direction of the photon's propagation. The photon also carries spin angular momentum that does not depend on its frequency. The magnitude of its spin is \sqrt{2} \hbar and the component measured along its direction of motion, its helicity, must be \pm\hbar. These two possible helicities correspond to the two possible circular polarization states of the photon (right-handed and left-handed).

To illustrate the significance of these formulae, the gamma rays lose energy while passing through matter.

The classical formulae for the energy and momentum of momentum per unit time.

Historical development

Main article: Light

 

In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, radio waves[22]—seemed to be the final blow to particle models of light.  

The photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.

At the same time, investigations of photoelectric effect, Einstein received the 1921 Nobel Prize in physics.

Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[5] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into point-like quanta that move independently of one another, even if the wave itself is spread continuously over space.[5] In 1909[6] and 1916,[8] Einstein showed that, if quantum electrodynamics and its successor, the Standard Model.

Early objections

 

Einstein's 1905 predictions were verified experimentally in several ways within the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[28] However, before absorption of light by atoms; their models agreed excellently with the spectrum of hydrogen, but not with those of other atoms. It was only the Compton scattering of a photon by a free electron (which can have no energy levels, since it has no internal structure) that convinced most physicists that light itself was quantized.

Even after Compton's experiment, Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.[29] To account for the then-available data, two drastic hypotheses had to be made:

  • Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation.
  • Causality is abandoned. For example, emissions induced by a "virtual" electromagnetic field.

However, refined Compton experiments showed that energy-momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his co-workers gave their model “as honorable a funeral as possible“.[27] Nevertheless, the BKS model inspired Werner Heisenberg in his development[30] of quantum mechanics.

A few physicists persisted[31] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter obeys the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by elegant photon-correlation experiments.[32] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.

Wave–particle duality and uncertainty principles

See also: Wave–particle duality, Squeezed coherent state, and Uncertainty principle

Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as Gauge boson sections below).

 

A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope.[34] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics

\Delta x \sim \frac{\lambda}{\sin \theta}

where θ is the aperture angle of the microscope. Thus, the position uncertainty Δx can be made arbitrarily small by reducing the wavelength. The momentum of the electron is uncertain, since it received a “kick” Δp from the light scattering from it into the microscope. If light were not quantized into photons, the uncertainty Δp could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals

\Delta p \sim p_{\mathrm{photon}} \sin\theta = \frac{h}{\lambda} \sin\theta

giving the product \Delta x \Delta p \, \sim \, h, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.

The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase φ of that wave

ΔnΔφ > 1

See coherent state and squeezed coherent state for more details.

Both photons and material particles such as electrons create analogous interference patterns when passing through a quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.

Bose–Einstein model of a photon gas

Main articles: Bose–Einstein statistics, and Spin-statistics theorem

In 1924, Bose–Einstein condensation was observed experimentally in 1995.[45]

Photons must obey Fermi-Dirac statistics or, equivalently, the Pauli exclusion principle, which states that at most one particle can occupy any given state. Thus, if the photon were a fermion, only one photon could move in a particular direction at a time. This is inconsistent with the experimental observation that lasers can produce coherent light of arbitrary intensity, that is, with many photons moving in the same direction. Hence, the photon must be a boson and obey Bose–Einstein statistics.

Stimulated and spontaneous emission

Main articles: Laser

 

In 1916, Einstein showed that Planck's quantum hypothesis E = hν could be derived from a kinetic rate equation.[7] Consider a cavity in electromagnetic radiation and systems that can emit and absorb that radiation. Thermal equilibrium requires that the number density ρ(ν) of photons with frequency ν is constant in time; hence, the rate of emitting photons of that frequency must equal the rate of absorbing them.

Einstein hypothesized that the rate Rji for a system to absorb a photon of frequency ν and transition from a lower energy Ej to a higher energy Ei was proportional to the number Nj of molecules with energy Ej and to the number density ρ(ν) of ambient photons with that frequency

R_{ji} = N_{j} B_{ji} \rho(\nu) \!

where Bji is the rate constant for absorption.

More daringly, Einstein hypothesized that the reverse rate Rij for a system to emit a photon of frequency ν and transition from a higher energy Ei to a lower energy Ej was composed of two terms:

R_{ij} = N_{i} A_{ij} + N_{i} B_{ij} \rho(\nu) \!

where Aij is the rate constant for induced or stimulated emission). Einstein showed that Planck's energy formula E = hν is a necessary consequence of these hypothesized rate equations and the basic requirements that the ambient radiation be in thermal equilibrium with the systems that absorb and emit the radiation and independent of the systems' material composition.

This simple kinetic model was a powerful stimulus for research. Einstein was able to show that Bij = Bji (i.e., the rate constants for induced emission and absorption are equal) and, perhaps more remarkably,

A_{ij} = \frac{8 \pi h \nu^{3}}{c^{3}} B_{ij}.

Einstein did not attempt to justify his rate equations but noted that Aij and Bij should be derivable from a “mechanics and electrodynamics modified to accommodate the quantum hypothesis”. This prediction was borne out in quantum mechanics and quantum electrodynamics, respectively; both are required to derive Einstein's rate constants from first principles. Paul Dirac derived the Bij rate constants in 1926 using a semiclassical approach,[46] and, in 1927, succeeded in deriving all the rate constants from first principles.[47][48] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;[49][50][51] the earlier quantum mechanics (the quantization of material particles moving in a potential) represents the “first quantization”.

Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of light-particle motion was first considered by birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow.[19] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[27] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[52][53] was inspired by Einstein's later work searching for a more complete theory.[54]

Second quantization

Main article: Quantum field theory

 

In 1910, Planck's law of black-body radiation from a relatively simple assumption.[55] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of hν, where ν is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.[6]

In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way.[56] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be E = nhν, where ν is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E = nhν as a state with n photons, each of energy hν. This approach gives the correct energy fluctuation formula.  

Dirac took this one step further.[47][48] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's Aij and Bij coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of black body radiation by assuming BE statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey BE statistics.

Dirac's second-order perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and positron pairs.

In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode

|n_{k_0}\rangle\otimes|n_{k_1}\rangle\otimes\dots\otimes|n_{k_n}\rangle\dots

where |n_{k_i}\rangle represents the state in which \, n_{k_i} photons are in the mode ki. In this notation, the creation of a new photon in mode ki (e.g., emitted from an atomic transition) is written as |n_{k_i}\rangle \rightarrow |n_{k_i}+1\rangle. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.

The photon as a gauge boson

Main article: Gauge theory

The electromagnetic field can be understood as a gauge theory, i.e., as a field that results from requiring that symmetry hold independently at every position in spacetime.[57] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of a complex number, which reflects the ability to vary the phase of a complex number without affecting real numbers made from it, such as the energy or the Lagrangian.

The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero quantum electrodynamics may also adopt unphysical polarization states.[57]

In the prevailing Standard Model of physics, the photon is one of four gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.

Photon structure

Main article: Quantum Chromodynamics

According to Quantum Chromodynamics, a real photon can interact both as a point-like particle, or as a collection of proton, but by fluctuations of the point-like photon into a collection of partons.[61]

Contributions to the mass of a system

See also: Mass in special relativity and Gravitation

The energy of a system that emits a photon is decreased by the energy E of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount E / c2. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount.

This concept is applied in a key prediction of QED, the theory of positronium.

Since photons contribute to the stress-energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound-Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.

Photons in matter

See also: Group velocity and Photochemistry

Light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. For example, photons suffer so many collisions on the way from the core of the sun that radiant energy can take about a million years to reach the surface;[62] however, once in open space, a photon only takes 8.3 minutes to reach Earth. The factor by which the speed is decreased is called the different speeds; this is called dispersion. The polariton propagation speed v equals its group velocity, which is the derivative of the energy with respect to momentum.

v = \frac{d\omega}{dk} = \frac{dE}{dp}

 

where, as above, E and p are the polariton's energy and momentum magnitude, and ω and k are its angular frequency and wave number, respectively. In some cases, the dispersion can result in Brillouin scattering.

Photons can also be photochemistry.

Technological applications

Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.

Individual photons can be detected by several methods. The classic semiconductors; an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.

Planck's energy formula E = hν is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the fluorescent light bulb can be designed using gas molecules with different electronic energy levels and adjusting the typical energy with which an electron hits the gas molecules within the bulb.

Under some conditions, an energy transition can be excited by two photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see two-photon excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.

In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and re-emits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, which is used to measure molecular distances.

Recent research

See also: Quantum optics

The fundamental nature of the photon is believed to be understood theoretically; the prevailing Standard Model predicts that the photon is a gauge boson of spin 1, without mass and without charge, that results from a local U(1) gauge symmetry and mediates the electromagnetic interaction. However, physicists continue to check for discrepancies between experiment and the Standard Model predictions, in the hope of finding clues to physics beyond the Standard Model. In particular, experimental physicists continue to set ever better upper limits on the charge and mass of the photon; a non-zero value for either parameter would be a serious violation of the Standard Model. However, all experimental data hitherto are consistent with the photon having zero charge[15] and mass.[63] The best universally accepted upper limits on the photon charge and mass are 5×10−52 kg (6x10-17 eV), respectively .[64]

Much research has been devoted to applications of photons in the field of quantum optics. Photons seem well-suited to be elements of an ultra-fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as two-photon absorption, self-phase modulation and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce single-photon states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.

See also

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References and footnotes

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  63. ^ (a) Goldhaber, AS (1971). "Terrestrial and Extraterrestrial Limits on The Photon Mass". Reviews of Modern Physics 43: 277–96..
    (b) Fischbach, E; Kloor H, Langel RA, Lui ATY, and Peredo M (1994). "New Geomagnetic Limits on the Photon Mass and on Long-Range Forces Coexisting with Electromagnetism". Physical Review Letters 73: 514–17..
    (c) Official particle table for gauge and Higgs bosons S. Eidelman et al. (Particle Data Group) Physics Letters B 592, 1 (2004)
    (d) Davis, L; Goldhaber AS and Nieto MM (1975). "Limit on Photon Mass Deduced from Pioneer-10 Observations of Jupiter's Magnetic Field". Physical Review Letters 35: 1402–1405..
    (e) Luo, J; Shao CG, Liu ZZ, and Hu ZK (1999). "Determination of the limit of photon mass and cosmic magnetic vector with rotating torsion balance". Physical Review A 270: 288–292..
    (f) Schaeffer, BE (1999). "Severe limits on variations of the speed of light with frequency". Physical Review Letters 82: 4964–4966..
    (g) Luo, J; Tu LC, Hu ZK, and Luan EJ (2003). "New experimental limit on the photon rest mass with a rotating torsion balance". Physical Review Letters 90: Art. No. 081801.
    (h) Williams, ER; Faller JE and Hill HA (1971). "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass". Physical Review Letters 26: 721–724.
    (i) Lakes, R (1998). "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential". Physical Review Letters 80: 1826.
    (j) 2006 PDG listing for photon W.-M. Yao et al. (Particle Data Group) Journal of Physics G 33, 1 (2006).
    (k) Adelberger, E; Dvali, G and Gruzinov, A. "Photon Mass Bound Destroyed by Vortices". Physical Review Letters 98: Art. No. 010402.
  64. ^ Official particle table for gauge and Higgs bosons Retrieved October 24, 2006

Additional references

  • Clauser, JF. (1974). "Experimental distinction between the quantum and classical field-theoretic predictions for the photoelectric effect". Phys. Rev. D 9: 853–860.
  • Kimble, HJ; Dagenais M, and Mandel L. (1977). "Photon Anti-bunching in Resonance Fluorescence". Phys. Rev. Lett. 39: 691–695. article web link
  • Grangier, P; Roger G, and Aspect A. (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences". Europhysics Letters 1: 501–504.
  • Thorn, JJ; Neel MS, Donato VW, Bergreen GS, Davies RE and Beck M. (2004). "Observing the quantum behavior of light in an undergraduate laboratory". American Journal of Physics 72: 1210–1219. http://people.whitman.edu/~beckmk/QM/grangier/grangier.html
  • Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press.  An excellent history of the photon's early development.
  • Ray Glauber's Nobel Lecture, “100 Years of Light Quanta”. Delivered 8 December 2005. Another history of the photon, summarized by a key physicist who developed the concepts of coherent states of photons.
  • Lamb, WE (1995). "Anti-photon". Applied Physics B 60: 77–84. Feisty, fun and sometimes snarky history of the photon, with a strong argument for allowing only its second-quantized definition, by Willis Lamb, the 1955 Nobel laureate in Physics.
  • Special supplemental issue of Optics and Photonics News (vol. 14, October 2003)
    • Roychoudhuri, C; Rajarshi R. "The nature of light: what is a photon?". Optics and Photonics News 14: S1 (Supplement).
    • Zajonc, A. "Light reconsidered". Optics and Photonics News 14: S2–S5 (Supplement).
    • Loudon, R. "What is a photon?". Optics and Photonics News 14: S6–S11 (Supplement).
    • Finkelstein, D. "What is a photon?". Optics and Photonics News 14: S12–S17 (Supplement).
    • Muthukrishnan, A; Scully MO, Zubairy MS. "The concept of the photon—revisited". Optics and Photonics News 14: S18–S27 (Supplement).
    • Mack, H; Schleich WP. "A photon viewed from Wigner phase space". Optics and Photonics News 14: S28–S35 (Supplement).
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Photon". A list of authors is available in Wikipedia.